Phase retrieval by hyperplanes

We show that a scalable frame does phase retrieval if and only if the hyperplanes of its orthogonal complements do phase retrieval. We then show this result fails in general by giving an example of a frame for $\mathbb R^3$ which does phase retrieval but its induced hyperplanes fail phase retrieval. Moreover, we show that such frames always exist in $\mathbb R^d$ for any dimension $d$. We also give an example of a frame in $\mathbb R^3$ which fails phase retrieval but its perps do phase retrieval. We will also see that a family of hyperplanes doing phase retrieval in $\mathbb R^d$ must contain at least $2d-2$ hyperplanes. Finally, we provide an example of six hyperplanes in $\mathbb R^4$ which do phase retrieval

Elevated alpha-synuclein caused by SNCA gene triplication impairs neuronal differentiation and maturation in Parkinson's patient-derived induced pluripotent stem cells

We have assessed the impact of α-synuclein overexpression on the differentiation potential and phenotypic signatures of two neural-committed induced pluripotent stem cell lines derived from a Parkinson´s disease patient with a triplication of the human SNCA genomic locus. In parallel, comparative studies were performed on two control lines derived from healthy individuals and lines generated from the patient iPS-derived neuroprogenitor lines infected with a lentivirus incorporating a small hairpin RNA to knock down the SNCA mRNA. The SNCA triplication lines exhibited a reduced capacity to differentiate into dopaminergic or GABAergic neurons and decreased neurite outgrowth and lower neuronal activity compared with control cultures. This delayed maturation phenotype was confirmed by gene expression profiling, which revealed a significant reduction in mRNA for genes implicated in neuronal differentiation such as delta-like homolog 1 (DLK1), gamma-aminobutyric acid type B receptor subunit 2 (GABABR2), nuclear receptor related 1 protein (NURR1), G-protein-regulated inward-rectifier potassium channel 2 (GIRK-2) and tyrosine hydroxylase (TH). The differentiated patient cells also demonstrated increased autophagic flux when stressed with chloroquine. We conclude that a two-fold overexpression of α-synuclein caused by a triplication of the SNCA gene is sufficient to impair the differentiation of neuronal progenitor cells, a finding with implications for adult neurogenesis and Parkinson´s disease progression, particularly in the context of bioenergetic dysfunction.Fil: Oliveira, L. M. A.. Max-Planck-Institut für biophysikalische Chemie; AlemaniaFil: Falomir Lockhart, Lisandro Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Bioquímicas de La Plata "Prof. Dr. Rodolfo R. Brenner". Universidad Nacional de la Plata. Facultad de Ciencias Médicas. Instituto de Investigaciones Bioquímicas de La Plata ; Argentina. Max-Planck-Institut für biophysikalische Chemie; AlemaniaFil: Botelho, M. G.. Max-Planck-Institut für biophysikalische Chemie; Alemania. Universidade Federal do Rio de Janeiro; BrasilFil: Lin, K. H.. Max-Planck-Institut für biophysikalische Chemie; AlemaniaFil: Wales, P.. Universität Göttingen; AlemaniaFil: Koch, J. C.. Universität Göttingen; AlemaniaFil: Gerhardt, Elizabeth. Universität Göttingen; AlemaniaFil: Taschenberger, H.. Max-Planck-Institut für biophysikalische Chemie; AlemaniaFil: Outeiro, T. F.. Universität Göttingen; AlemaniaFil: Lingor, P.. Universität Göttingen; AlemaniaFil: Schüele, B.. The Parkinson’s Institute; Estados UnidosFil: Arndt Jovin, D. J.. Max-Planck-Institut für biophysikalische Chemie; AlemaniaFil: Jovin, T. M.. Max-Planck-Institut für biophysikalische Chemie; Alemani

Divergência genética entre genótipos de sorgo sacarino usando técnicas multivariadas.

Objetivou-se avaliar a divergência genética entre genótipos de sorgo sacarino por meio de técnicas multivariadas. Foram avaliados 45 genótipos de sorgo sacarino em Lavras-MG. O delineamento experimental foi o alfa-látice 9x5, com três repetições. As parcelas consistiram de duas linhas de 5 metros espaçadas 0,60 metros. Foram mensurados os seguintes caracteres: número de dias para o florescimento, altura de planta (m), massa de panícula (g), produção de massa verde (t/ha), teor de sólidos solúveis totais (%caldo), toneladas de brix por hectare e produção de etanol (L/ha). Procederam-se as análises de variância associado ao teste F a 5% de probabilidade. A diversidade genética foi avaliada com base na distância de Mahalanobis com posterior agrupamento dos genótipos pelo método de Tocher, bem como pelo método das variáveis canônicas (CRUZ; CARNEIRO, 2006). Houve divergência genética entre os genótipos de sorgo sacarino quanto aos caracteres estudados. As técnicas multivariadas utilizadas possibilitaram a formação de três grupos bem definidos e concordantes, com destaque para a linhagem CMSXS643R por apresentar desempenho agronômico e industrial favoráveis